2. Data and Statistics:
Descriptive and Inferential
Approaches
Understanding How Data Becomes
Meaning
STAT 200: Statistics and Evaluation in Education
Presented by: MARY ROSE M. HERNANDEZ
June 21, 2025 / Saturday / Via Online
4. S T A T I S T I C S
It is the branch of mathematics that deals with
collecting, organizing, analyzing, and interpreting data
to help us understand information and make better
decisions.
• 📥 Collects data from surveys, experiments, or
observations, etc.
• ️
🗂️Organizes data into charts, graphs, and tables
• 🧠 Analyzes data to find patterns and trends
• ️
🗣️Interprets results to make decisions and
predictions
5. • Data refers to individual pieces of
factual information collected through
observation, measurement, research, or
inquiry.
• In statistics, data are the raw materials
used to summarize, interpret, and make
decisions about real-world situations.
Understanding Data: The Foundation of Statistics
6. • 📊 To describe patterns or distributions
(descriptive)
• 🔍 To infer or predict outcomes (inferential)
• 🔄 To compare or relate variables
• 💡 To inform decision-making in fields such
as education, business, health, and public
policy
Purpose of Data in Statistics:
7. Characteristics of Quality Data:
Characteristic Description
Relevant Directly connected to the problem or
question
Accurate Truthful and verified
Complete No missing or vague entries
Timely Collected and used within a useful time
frame
Consistent Standardized format, variables, and
measurements
8. Sources of Data:
📝 Primary Data –
Collected firsthand via:
📚 Secondary Data –
Collected by others:
• Surveys
• Observations
• Experiments
• Interviews
• Government databases
• Journal articles
• Company records
• Research repositories
9. Types of Data in Statistical Analysis
Qualitative Data
(Categorical)
Quantitative Data
(Numerical)
• Definition:
Describes non-numeric
characteristics or
categories
• Purpose: To group,
label, or categorize
observations
• Definition: Expressed
in numbers and can be
measured or counted
• Purpose: To analyze
numerical relationships
and apply statistical
tests
10. Types of Data in Statistical Analysis
Qualitative Data
(Categorical)
Quantitative Data
(Numerical)
Subtypes:
• Nominal: No natural order
(e.g., gender, religion, eye
color)
• Ordinal: With logical order
(e.g., education level,
satisfaction ratings)
Subtypes:
• Discrete: Countable
values (e.g., number of
books read, exam
attempts)
• Continuous: Measurable
values with decimals (e.g.,
height, weight, GPA)
12. 1. Analyzing Data
• 🔍 Qualitative Data:
Analyzed through frequencies, proportions, and cross-
tabulations
Often used in thematic analysis, coding, or content analysis
in qualitative research
• 📊 Quantitative Data:
Analyzed using descriptive and inferential techniques
Examples: mean, standard deviation, regression, t-tests,
ANOVA
How We Use Different Types of Data
13. 2. Comparing Data
• 📊 Qualitative:
Compare categories or groups using bar charts or chi-square
tests
Example: Comparing preferences between teaching styles
• 📈 Quantitative:
Compare numerical trends using means, medians, box plots,
or hypothesis testing
Example: Comparing average exam scores between two
sections
How We Use Different Types of Data
15. 4. Implications for Statistical Methods
✅ The type of data determines:
• Which summary measures are valid (mean vs. mode)
• Which graphs are most appropriate
• Which statistical tests are applicable (e.g., chi-square
for nominal data, t-test for interval/ratio data)
❗ Misclassifying data can lead to invalid
conclusions or misuse of methods
How We Use Different Types of Data
17. Levels of Measurement: Understanding Data Scales
🧠 Examples in Context:
• 🏫 Nominal: What college course are you enrolled
in? → (Math, Science, English)
• 🪜 Ordinal: Rate your satisfaction from 1 (Very
Dissatisfied) to 5 (Very Satisfied)
• ️
🌡️Interval: Room temperature recorded daily over
a week
• 📏 Ratio: Student scores on a 100-point test
18. Two Major Types of Statistics
Descriptive Statistics Inferential Statistics
Summarizes and describes
data.
Deals with known data only.
Uses charts, graphs, averages,
etc.
Example: Class average score
Makes predictions or generalizations
about a population
Works with samples to estimate for
populations
Uses probability, estimation, and
hypothesis testing
Example: Predicting national exam results
from a sample
19. Two Major Types of Statistics
Descriptive Statistics Inferential Statistics
helps us
summarize data
we already have.
helps us make
guesses or
decisions based on
part of the data.
20. • 🎯 Describes the main features of a dataset
• 📊 Summarizes data using numbers, tables,
and visuals
• 🔢 Focuses on what the data shows, not what
it predicts
• 📌 Used to organize and simplify raw
information
Understanding Descriptive Statistics
21. “If we recorded the test scores of 30
students, descriptive statistics would help us
know:
• What’s the average score?
• What’s the highest and lowest score?
“Descriptive statistics tells us what’s going on right
now in the data — no guessing, just describing.”
22. 📌 Descriptive statistics includes tools such as:
• Measures of Central Tendency
(e.g., mean, median, mode) — describe the “center” of
the data
• Measures of Dispersion
(e.g., range, standard deviation) — show how spread
out the data is
• Data Presentation Methods
(e.g., tables, bar graphs, histograms, pie charts)
Overview of Descriptive Techniques
23. Main Points:
• 🔍 Goes beyond the data — it draws conclusions
and makes predictions
• 🎯 Works with samples to make generalizations
about a larger population
• 🎲 Uses probability theory to ensure accuracy of
conclusions
• ⚖️Helps with decision-making under uncertainty
Introduction to Inferential Statistics
24. A researcher surveys 100 students about
their study habits. With inferential statistics,
they estimate how all students in the
university study — not just the 100
surveyed.
“Inferential statistics allows us to make educated
guesses about a larger group, based on a smaller
group.”
25. 👥 Population
• The entire group you want to study or make conclusions about
• Example: All college students in your university
🎯 Sample
A smaller, representative group taken from the population
Example: 200 randomly selected students from your university
🔄 Why use a sample?
Studying the whole population is often impossible, expensive, or time-
consuming
A well-chosen sample allows us to make informed guesses about the
population
Population and Sample: What's the Difference?
26. If a school has 5,000 students and you
survey only 150, the 5,000 is your
population, and the 150 is your
sample.
“A sample is a small slice of the population — and if
chosen well, it can tell us a lot.”
27. 🎲 What is Random Sampling?
• Every individual in the population has an equal chance of
being selected
• Ensures the sample is unbiased and representative
🧪 Why is it important?
• Helps avoid selection bias
• Makes statistical results more accurate and reliable
• Supports valid generalizations from sample to population
🧭 Without it?
• Results may reflect only certain groups
• Can lead to wrong conclusions and poor decisions
Why Random Sampling Matters
28. 📌 The next few topics are essential to
inferential statistics:
• Estimating population parameters
• Testing hypotheses
• Understanding p-values and significance
levels
Estimation, Hypothesis Testing & Statistical Significance
29. 🎓 A professor wants to know if two sections of a graduate class performed
differently on the final exam.
• Population: All students enrolled in both sections
• Sample Data:
Section A (n = 30): Mean = 85
Section B (n = 28): Mean = 81
📊 Using inferential statistics, the professor tests whether this difference in
means is statistically significant or due to random variation.
🧠 Conclusion:
If the test shows the difference is significant, the professor may conclude that
one section performed better — not just by chance, but due to real factors
(e.g., teaching style, resources).
Example of Inferential Statistics
30. Descriptive Statistics Inferential Statistics
Used to summarize known
data
No assumptions beyond the
data
Example: Average score of
students in your class
Answers: “What does the data
show?”
Used to make predictions or
generalizations.
Involves probability and
uncertainty
Example: Predicting exam results
for all students in the university
Answers: “What can we say about a
bigger group?”
When to Use Descriptive and Inferential Statistics
32. 32
“The average points per game of
the team this season is 92.3.”
✅ Descriptive
(Summarizes collected data)
33. 33
“Based on recent polls, 65% of
voters will support Candidate A in
the next election.”
✅ Inferential
(Makes a prediction)
34. 34
“A study of 150 people suggests
that 70% of the population is likely
to support the new policy.”
✅ Inferential
(Generalizing from a sample to a population)
35. 35
✅ Descriptive
(They use statistics for just summarizing data or records of the
baseball game. They didn’t make any conclusions or inferences.)
40. 🟩 Main Points:
📊 Statistics helps us make sense of data and supports
decision-making
📂 Data is the foundation of all statistical analysis — it must
be collected, classified, and understood before anything else
🧾 Descriptive statistics summarizes and presents data
clearly
🔮 Inferential statistics allows us to make predictions and
test ideas
🎯 Choosing the right method depends on your goal: describe
or infer
Key Takeaways
41. CREDITS: This presentation template was created by Slidesgo, and
includes icons by Flaticon, and infographics & images by Freepik
41
Thanks!
Editor's Notes
#4: Statistics is like a toolbox that helps us solve real-world problems using data.
It's used in business, science, education, sports, health care, and more.
#5: Factual information refers to data that is objective, verifiable, and based on real events, observations, or measurements—not opinions, beliefs, or assumptions.
🔍 Characteristics of Factual Information:
✅ Truth-Based – It reflects something that actually happened or exists.
Example: “The student scored 85% on the math test.”
📏 Measurable or Observable – It can be collected using tools, surveys, or scientific methods.
Example: Measuring the height of students using a tape measure.
🔄 Repeatable/Verifiable – Other people can confirm it using the same methods.
Example: If multiple observers record the same temperature in a classroom, it's verifiable.
❌ Not Subjective – Unlike opinions (“Math is boring”), factual information doesn’t rely on feelings or personal perspectives.
🎯 Why Is Factual Information Important in Statistics?
It ensures accuracy and reliability of results.
It supports evidence-based decisions in areas like education, health, and public policy.
It eliminates bias and allows clear communication of findings.
In statistics, if the information is not factual, the analysis can lead to false conclusions.
In statistics, data are often called the “raw materials” of analysis. This term comes from the idea used in manufacturing and cooking: just like raw materials are the basic inputs used to create a finished product, data are the basic inputs used to produce statistical information and insights.
#9:
Qualitative data describe non-numeric characteristics or categories.
They capture qualities, attributes, or labels rather than measurable amounts.
#10: Nominal data are categorical data with no natural order or ranking.
They are used to label, name, or identify different items or groups, but they cannot be meaningfully sorted.
📌 Key Points:
You cannot average or rank nominal data.
Useful for grouping and classification.
#19: Descriptive is like telling a story about the data you already collected.
Inferential is like using a few puzzle pieces to guess what the full picture looks like.
Both are important — one helps describe, the other helps decide.
#21: Think of it like a report card—it summarizes your performance, but doesn’t predict what’s next.
It's the first step in any data analysis — we describe first before we make any conclusions.
#22: "Each of these tools will be explained in more detail by other presenters."
#24: Emphasize that we can’t always study an entire population, so we use a sample.
Inferential statistics bridges the gap between what we know (sample) and what we want to know (population).
It’s essential in research, where predictions or testing theories are involved.
#26: Reinforce that inferential statistics depends on working with a sample to infer conclusions about the population.
Mention that how we choose the sample (randomly or not) can greatly affect the reliability of our results — a nice transition into the next slide on random sampling.
#27: Use this to remind your audience that good data starts with good sampling.
In real research, randomness is what allows us to confidently generalize results.
You can mention that this connects to ethics in research, too — ensuring fairness and objectivity.
#29: Emphasize that inferential statistics lets us go beyond the numbers and draw insights that matter.
You can connect this to research or teaching: we often don't work with whole populations, so we rely on sample-based decisions.
#30: This is where you tie everything together: we often use both types in a full analysis.
Descriptive is the first step (what we know), and inferential is the next step (what we want to know).
